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Orgel and Dembski Redux

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A couple of months ago I quoted from Lesli Orgel’s 1973 book on the origins of life.  L. E. Orgel, The Origins of Life: Molecules and Natural Selection (John Wiley & Sons, Inc.; New York, 1973).  I argued that on page 189 of that book Orgel used the term “specified complexity” in a way almost indistinguishable from the way Bill Dembski has used the term in his work.  Many of my Darwinian interlocutors demurred.  They argued the quotation was taken out of context and that Orgel meant something completely different from Dembski.  I decided to order the book and find out who was right.  Below, I have reproduced the entire section in which the original quotation appeared.  I will let readers decide whether I was right.  (Hint: I was).

 

All that follows is a word-for-word reproduction of the relevant section from Orgel’s book:

 

[Page 189]

Terrestrial Biology

Most elementary introductions to biology contain a section on the nature of life.  It is usual in such discussions to list a number of properties that distinguish living from nonliving things. Reproduction and metabolism, for example, appear in all of the lists; the ability to respond to the environment is another old favorite.  This approach extends somewhat the chef’s definition “If it quivers, it’s alive.” Of course, there are also many characteristics that are restricted to the living world but are not common to all forms of life.  Plants cannot pursue their food; animals do not carry out photosynthesis; lowly organisms do not behave intelligently.

It is possible to make a more fundamental distinction between living and nonliving things by examining their molecular structure and molecular behavior.  In brief, living organisms are distinguished by their specified complexity.*· Crystals are usually taken as the prototypes of simple, well-specified structures, because they consist of a very large number of identical molecules packed together in a uniform way.  Lumps of granite or random mixtures of polymers are examples of structures which are complex but not specified.  The crystals fail to qualify as living because they lack complexity, the mixtures of polymers fail to qualify because they lack specificity.

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* It is impossible to find a simple catch phrase to capture this complex idea.  “Specified and. therefore repetitive complexity” gets a little closer (see later).

[Page 190]

These vague ideas can be made more precise by introducing the idea of information.  Roughly speaking, the information content of a structure is the minimum number of instructions needed to specify the structure.  One can see intuitively that many instructions are needed to specify a complex structure.  On the other hand, a simple repeating structure can be specified in rather few instructions.  Complex but random structures, by definition, need hardly be specified at all.

These differences are made clear by the following example.  Suppose a chemist agreed to synthesize anything that could describe [sic] accurately to him.  How many instructions would he need to make a crystal, a mixture of random DNA-like polymers or the DNA of the bacterium E. coli?

To describe the crystal we had in mind, we would need to specify which substance we wanted and the way in which the molecules were to be packed together in the crystal.  The first requirement could be conveyed in a short sentence.  The second would be almost as brief, because we could describe how we wanted the first few molecules packed together, and then say “and keep on doing the same.”  Structural information has to be given only once because the crystal is regular.

It would be almost as easy to tell the chemist how to make a mixture of random DNA-like polymers.  We would first specify the proportion of each of the four nucleotides in the mixture.  Then, we would say, “Mix the nucleotides in the required proportions, choose nucleotide molecules at random from the mixture, and join them together in the order you find them.”  In this way the chemist would be sure to make polymers with the specified composition, but the sequences would be random.

It is quite impossible to produce a corresponding simple set of instructions that would enable the chemist to synthesize the DNA of E. coli.  In this case, the sequence matters; only by specifying the sequence letter-by-letter (about 4,000,000 instructions) could we tell the chemist what we wanted him to make.  The synthetic chemist would need a book of instructions rather than a few short sentences.

It is important to notice that each polymer molecule in a random mixture has a sequence just as definite as that of E.

[Page 191]

coli DNA.  However, in a random mixture the sequences are not specified, whereas in E. coli, the DNA sequence is crucial.  Two random mixtures contain quite different polymer sequences, but the DNA sequences in two E. coli cells are identical because they are specified.  The polymer sequences are complex but random; although E. coli DNA is also complex, it is specified in a unique way.

The structure of DNA has been emphasized here, but similar arguments would apply to other polymeric materials.  The protein molecules in a cell are not a random mixture of polypeptides; all of the many hemoglobin molecules in the oxygen-carrying blood cells, for example, have the same sequence.  By contrast, the chance of getting even two identical sequences 100 amino acids long in a sample of random polypeptides is negligible.  Again, sequence information can serve to distinguish the contents of living cells from random mixtures of organic polymers.

When we come to consider the most important functions of living matter, we again find that they are most easily differentiated from inorganic processes at the molecular level.  Cell division, as seen under the microscope, does not appear very different from a number of processes that are known to occur in colloidal solutions.  However, at the molecular level the differences are unmistakable:  cell division is preceded by the replication of the cellular DNA.  It is this genetic copying process that distinguishes most clearly between the molecular behavior of living organisms and that of nonliving systems.  In biological processes the number of information-rich polymers is increased during growth; when colloidal droplets “divide” they just break up into smaller droplets.

Comments
fifthmonarchyman: I would say that the string that I posted has 0 probability of happening by chance and infinite K-complexity when considered from an algorithmic starting point. That is incorrect. Given arithmetic, there is a simple algorithm which can calculate the series. You provided one yourself. 4 * sum for n = 1 to infinity of ((n mod 2 * 2 ) - 1) / (n * 2 - 1)Zachriel
January 25, 2015
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zac says, Anything that can solve problems can be treated as an oracle. I say, The problems need to include "halting problems", Are you actually claiming that evolution can solve halting problems? zac says, It’s not clear evolution is algorithmic as there is a great deal of simultaneity involved, more like a neutral network. I say, Are you claiming that evolution is conscious? zac says, That makes it {God} unbounded K-complexity, not zero. That’s because its shortest description is at least as long as an exhaustive list of its operations I say, There is no exhaustive list. just as there are no inner workings. An oracle is a black box when viewed from a algorithmic perspective So the K-complexity is zero. you say Just because you call it a black box doesn’t mean it doesn’t entail complexity I say I'm not necessarily claiming here that God is not complex. Although I would claim he is simple. I'm claiming that he like any oracle or axiom is not K-complex. peacefifthmonarchyman
January 25, 2015
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Zac says, Complexity measures don’t work that way. A given measure may be finite while another may be infinite. I say I would say that the string that I posted has 0 probability of happening by chance and infinite K-complexity when considered from an algorithmic starting point. However if an oracle specifies the string with the constant/Axiom Pi it can be described very easily. Here is an easier one. look at this string 8675309 The probability is .000001 The k-complexety from an algorithmic starting point a is few bytes larger than the length of the string itself. However Jenny and Tommy Tutone know that number so they could specify it with much less K-complexety. Something like J's# would work The deep connection between the k-complexety of Jenny's specification and the probability of the string occurring by chance is what CSI is all about. peacefifthmonarchyman
January 25, 2015
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fifthmonarchyman: Since God is not algorithmic he adds zero to the K-complexety. That makes it unbounded K-complexity, not zero. That's because its shortest description is at least as long as an exhaustive list of its operations. fifthmonarchyman: You’re the one who insisted that the use of oracles didn’t add complexity to the system. Z: Just because you call it a black box doesn’t mean it doesn’t entail complexity. There are even complexity classes for oracle machines. In any case, the minimal descriptive complexity is at least equal to the information passed through the interface. fifthmonarchyman: Are you now claiming that “Evolution” is an oracle? Anything that can solve problems can be treated as an oracle. fifthmonarchyman: That is quite a claim for an algorithmic process like “Evolution” wouldn’t you agree. It's not clear evolution is algorithmic as there is a great deal of simultaneity involved, more like a neutral network.Zachriel
January 25, 2015
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Zac said, You’re the one who insisted that the use of oracles didn’t add complexity to the system. I say, Are you now claiming that "Evolution" is an oracle? quote: an oracle machine can be visualized as a Turing machine with a black box, called an oracle, which is able to decide certain decision problems in a single operation. The problem can be of any complexity class. Even undecidable problems, like the halting problem, can be used. end quote: from here http://en.wikipedia.org/wiki/Oracle_machine That is quite a claim for an algorithmic process like "Evolution" wouldn't you agree. peacefifthmonarchyman
January 25, 2015
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zac said, God did it through gravity is more complex than God did it. The former includes two entities, while the latter only includes one I say. Again K-complexety is only interested in the length of the algorithm. Since God is not algorithmic he adds zero to the K-complexety. Please if you disagree with this stament explain why. Don't Just keep repeating yourself How would you quantify the K-complexety of a Turing Oracle? peacefifthmonarchyman
January 25, 2015
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fifthmonarchyman: If that sentiment was expressed more often by the powers that be you would have a much less restless and more content populace when it comes to Darwinian Evolution. Doubtful. Creationism is an entrenched social and cultural phenomenon. fifthmonarchyman: Pi has a precise meaning. It only has a precise meaning with regards to K-complexity if you allow it in the language. fifthmonarchyman: The meaning of the term “evolution” keeps evolving as new detail is required. unless you want define evolution as simply change over time. You're the one who insisted that the use of oracles didn't add complexity to the system. fifthmonarchyman: I can measure age with carbon dating or by counting tree rings I will just need to calibrate as the need arises. Complexity measures don't work that way. A given measure may be finite while another may be infinite.Zachriel
January 25, 2015
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wow zac here goes Zac says, it’s unlikely to ever be complete in any real sense, certainly not in the near term. I say, I tell you this as a Darwin critic and a fundi. If that sentiment was expressed more often by the powers that be you would have a much less restless and more content populace when it comes to Darwinian Evolution. Instead what we usually get is something like "NeoDarwinism has explained the panorama of life with out the need for a designer" you say, That is true, but if we admit the description word “evolution” into the language, then it is only one word, just like pi is only one word. I say, Pi has a precise meaning. The meaning of the term “evolution” keeps evolving as new detail is required. unless you want define evolution as simply change over time. If you did that even rabid YECs would be happy with that term. you say, No scientific test for God did it has been developed. I say, Here is one. If God did it he must have different attributes than Zac ;-) you say, K-complexity can only be evaluated in a given description language, so you have to specify the language. I say, In order to make this easy you are free to choose your own language. just tell me which one you used once you do that translation into any language is not much of a problem. you say, Similarity is not the same as being equal. I say, I completely agree. If two measurements are similar we can use one as a proxy for the other as long as we make note of the differences as they arise. I can measure age with carbon dating or by counting tree rings I will just need to calibrate as the need arises. peacefifthmonarchyman
January 25, 2015
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fifthmonarchyman: So if I said that Darwinism in it’s most recent form is incomplete to adequately explain the panorama of life you would agree. If the theory of evolution were complete, there would be no need for evolutionary biologists. fifthmonarchyman: Better yet if I said any materialistic model that could possibly be offered to explain the panorama of life is destined to be incomplete you would agree. Sure, especially as evolutionary theory includes an historical component, it's unlikely to ever be complete in any real sense, certainly not in the near term. fifthmonarchyman: Not when measured by K complexety That is incorrect. God did it through gravity is more complex than God did it. The former includes two entities, while the latter only includes one. fifthmonarchyman: I have already shown a scholarly case can be made that all measures of complexity are equivalent That is incorrect. For instance, algorithmic complexity is not equivalent to effective complexity or logical depth. fifthmonarchyman: Zac did it could also be inserted for anything and everything and just like the hypothesis that God did it we can propose scientific ways of testing the claim. No scientific test for God did it has been developed. fifthmonarchyman: I’m not saying that the expansion of Pi requires additional K-complexity I’m saying that instruction to halt the algorithm at a certain digit requires additional k-complexity. It requires precisely one number. fifthmonarchyman: on the other hand the specification “Pi” is not subject to this weakness because we know it is an irrational constant and it can therefore be treated as an axiom in our model If pi is a member of the description language, then it is simpler than the algorithm, however, you had said the K-complexity of the algorithm was unbounded, which was incorrect. fifthmonarchyman: By the same token When it comes to a model for evolution each additional detail that is added to the RM plus NS core will require a longer description and thus is more K-complex. That is true, but if we admit the description word "evolution" into the language, then it is only one word, just like pi is only one word. fifthmonarchyman: the answers that they came up with for how to measure complexity bear a considerable similarity to each other. Similarity is not the same as being equal. fifthmonarchyman: What is their K-complexity? K-complexity can only be evaluated in a given description language, so you have to specify the language.Zachriel
January 25, 2015
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a little more on topic keith S said In that quote, Lloyd is referring to “complexity” as used by mainstream scientists and mathematicians, not Dembski’s idiosyncratic usage where “complexity” actually means “improbability”. I say, consider the following string of digits with zero entropy 3.141592653589793238462643383279502884197169399375105820974944592307816406286...... two questions What is the probability that they will occur by chance? What is their K-complexity? peacefifthmonarchyman
January 25, 2015
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keith's said, In that quote, Lloyd is referring to “complexity” as used by mainstream scientists and mathematicians, not Dembski’s idiosyncratic usage where “complexity” actually means “improbability”. I say, I'm not discussing CSI right now. I'm discussing using K-complexety to measure the complexity of a given model. So Lloyd's comment is very germane to my point. I realize that this overall thread is about CSI so you can ignore my off topic digressions if you wish. As far as complexity in CSI goes I think you know my position. Agree to disagree Peacefifthmonarchyman
January 25, 2015
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keith s says 1. The two answers are equal only if the expansion goes on forever. I say, Again you are missing the contribution of the oracle. When I deal with Pi I can treat it like a natural number I don't need to do the math I simply plug in the value with the resolution I need. An algorithm on the other hand does not have that option You say, The Kolmogorov complexity of the expansion is fixed. It doesn’t “grow forever”. I say Here is where I think I might have been a little unclear, I agree that the K-complexety of 4*(1 – 1/3 + 1/5 – 1/7 + …)is fixed that is not my argument. My argument is that 4*(1 – 1/3 + 1/5 – 1/7 + …) is not enough to compute the ratio of a actual phyiscal circle’s circumference to its diameter. To describe the ratio of an individual physical circle you need to add a function to halt the algorithm at a given resolution then you need to add additional descriptive language to model the places where the circle deviates from the original algorithm all of these add additional K-complexity. That complexity will grow until you reach the limits of your measurement system You say 3. The Kolmogorov complexity is determined by the shortest description of an entity using the given description language. Since “Pi” and the Taylor series expansion refer to the same number, their Kolmogorov complexities with respect to any particular description language are equal. I say, As I said before you are missing the contribution of the oracle. Pi is only a valid term when you know what it means. I hope I am making myself clear now. I appreciate the feed back. Once I grasp a concept I often simply assume that everyone else can see what I see. I struggle at times with clear explanation. peacefifthmonarchyman
January 25, 2015
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fifthmonarchyman:
I’m referring to Seth Lloyd’s claim.
In that quote, Lloyd is referring to "complexity" as used by mainstream scientists and mathematicians, not Dembski's idiosyncratic usage where "complexity" actually means "improbability".
Are you saying that you think that Dembski is more of an authority on complexity measures than a professor of mechanical engineering at the MIT?
No, I'm saying that despite all his faults, even Dembski understands the difference between Kolmogorov complexity and improbability:
But given nothing more than ordinary probability theory, Kolmogorov could at most say that each of these events had the same small probability of occurring, namely 1 in 2^100, or approximately 1 in 10^30. Indeed, every sequence of 100 coin tosses has exactly this same small probability of occurring. Since probabilities alone could not discriminate E sub R from E sub N, Kolmogorov looked elsewhere. Where he looked was computational complexity theory. The Design Inference, p. 169
Take some time to learn about Kolmogorov complexity, FMM. It's a really interesting subject.keith s
January 24, 2015
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fifthmonarchyman:
It’s possible I did not make myself clear enough at the outset. I understand your point but you are misunderstanding mine. I’m not saying that the expansion of Pi requires additional K-complexity I’m saying that instruction to halt the algorithm at a certain digit requires additional k-complexity.
No, here's what you said:
suppose I wanted to calculate the the K-complexety of the answer to this question “what is the ratio of a circle’s circumference to its diameter?” We could start out by trying to square the circle and end up with an algorithm like this 4*(1 – 1/3 + 1/5 – 1/7 + …) The k-complexity using this approach is huge and grows forever as more detail is needed. On the other hand we could answer the question with the following solution “Pi”
You're making multiple mistakes here. 1. The two answers are equal only if the expansion goes on forever. 2. The Kolmogorov complexity of the expansion is fixed. It doesn't "grow forever". 3. The Kolmogorov complexity is determined by the shortest description of an entity using the given description language. Since "Pi" and the Taylor series expansion refer to the same number, their Kolmogorov complexities with respect to any particular description language are equal.keith s
January 24, 2015
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@ Keith S It's possible I did not make myself clear enough at the outset. I understand your point but you are misunderstanding mine. I'm not saying that the expansion of Pi requires additional K-complexity I'm saying that instruction to halt the algorithm at a certain digit requires additional k-complexity. on the other hand the specification "Pi" is not subject to this weakness because we know it is an irrational constant and it can therefore be treated as an axiom in our model By the same token When it comes to a model for evolution each additional detail that is added to the RM plus NS core will require a longer description and thus is more K-complex. I hope that clarification is sufficient You say, No. Dembski understands this I say, I am not particularly bound by Dembski's opinion one way or another. Especially given the newness of the whole enterprise. Ideas are in flux and can be modified as the result of discussion and contemplation. I'm referring to Seth Lloyd's claim. quote: An historical analog to the problem of measuring complexity is the problem of describing electromagnetism before Maxwell's equations. In the case of electromagnetism, quantities such as electric and magnetic forces that arose in different experimental contexts were originally regarded as fundamentally different. Eventually it became clear that electricity and magnetism were in fact closely related aspects of the same fundamental quantity, the electromagnetic field. Similarly, contemporary researchers in architecture, biology, computer science, dynamical systems, engineering, finance, game theory, etc., have defined different measures of complexity for each field. Because these researchers were asking the same questions about the complexity of their different subjects of research, however, the answers that they came up with for how to measure complexity bear a considerable similarity to each other. end quote: from here http://web.mit.edu/esd.83/www/notebook/Complexity.PDF Are you saying that you think that Dembski is more of an authority on complexity measures than a professor of mechanical engineering at the MIT? peacefifthmonarchyman
January 24, 2015
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keiths:
Kolmogorov complexity is about the length of the description, not about the length of the computation.
fifthmonarchyman:
Of course but the description is simply an algorithm to compute the model.
The description and the computation are distinct, which is why your statement about the expansion of pi was incorrect:
The k-complexity using this approach is huge and grows forever as more detail is needed.
The Kolmogorov complexity doesn't grow at all, because the algorithm doesn't change. The description is finite, but the expansion is infinite. The algorithm is distinct from the result. Likewise, this description of the natural numbers is finite:
1. 0 is a natural number. 2. If n is a natural number, then n+1 is a natural number.
The description is short and simple, but the set being described is infinite. Low Kolmogorov complexity, large size.
Not when measured by K complexety and as I have already shown a scholarly case can be made that all measures of complexity are equivalent
No. Dembski understands this. Reread this quote.keith s
January 24, 2015
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Think, Joe. A crystal consists of a unit cell repeated many times in a specific spatial pattern. Orgel explains it in the very passage that Barry quoted in the OP:
Crystals are usually taken as the prototypes of simple, well-specified structures, because they consist of a very large number of identical molecules packed together in a uniform way.
To specify a cylindrical crystal of pure silicon, you would merely need to 1. Specify the unit cell. 2. Specify the spatial pattern for adding new unit cells to an existing crystal. 3. Specify the boundaries of the cylindrical crystal (to stop adding unit cells when the crystal has reached the desired size and shape). The crystal's simple description gives it a low Kolmogorov complexity. However, such a crystal is highly unlikely to form spontaneously, giving it a high specified complexity by Dembski's metric. Kolmogorov complexity is obviously not the same as Dembski's specified complexity. Barry, KF and fifthmonarchyman got it wrong.keith s
January 24, 2015
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I challenge keith s to provide the Kolmogorov complexity of a "cylindrical crystal of pure silicon" or stop using it as it is clear he doesn't have a clue. Show your work, keith.Joe
January 24, 2015
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zac said We merely pointed out that God did it can be inserted for anything, and by the standard you set, can be inserted for everything. I say Zac did it could also be inserted for anything and everything and just like the hypothesis that God did it we can propose scientific ways of testing the claim. Do you think we can not test the claim that Zac did X? peacefifthmonarchyman
January 24, 2015
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Zac, All scientific theories are incomplete by nature. I say, So if I said that Darwinism in it's most recent form is incomplete to adequately explain the panorama of life you would agree. Better yet if I said any materialistic model that could possibly be offered to explain the panorama of life is destined to be incomplete you would agree. Correct? now we are getting somewhere you say, More complicated. I say, Not when measured by K complexety and as I have already shown a scholarly case can be made that all measures of complexity are equivalent peacefifthmonarchyman
January 24, 2015
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fifthmonarchyman: By the same token Darwinism is offered as model for the Panorama of life and because it is an algorithm it can never get you there. All scientific theories are incomplete by nature. They're not judged by a standard of perfection, but of utility and explanatory power. fifthmonarchyman: If you define scientific as algorithmic then only algorithmic models qualify. We did no such thing. We merely pointed out that God did it can be inserted for anything, and by the standard you set, can be inserted for everything. fifthmonarchyman: What about God did it using gravity? More complicated. fifthmonarchyman: Of course but the description is simply an algorithm to compute the model. The algorithm is the model.Zachriel
January 24, 2015
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Keith S says Kolmogorov complexity is about the length of the description, not about the length of the computation I say Of course but the description is simply an algorithm to compute the model. peacefifthmonarchyman
January 24, 2015
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Zac says By that standard the simplest model of planetary movement is God did it, much simpler than gravity I say, What about God did it using gravity? This is just as simple computationally speaking as gravity but unlike gravity alone it is completely sufficient to explain the phenomena, peacefifthmonarchyman
January 24, 2015
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Zac says By that standard the simplest model of planetary movement is God did it, I say If you ask a classical musician how they got to Carnegie hall the simplest model is Practice!!!!! It is simple and it is complete and it is valid it just lacks comprehensive detail. Of course you could try to square the circle and propose an alternative algorithmic model that has more detail but can never be complete No specific step by step procedure or formula no matter how complex will ever get a musician to Carnegie hall there are intangibles that will always come into play. By the same token Darwinism is offered as model for the Panorama of life and because it is an algorithm it can never get you there. It will always fall short it will always need additional tweaks each with ever more computational costs. You say, (Of course, that’s not a scientific explanation, or even a scientific description, but that should be apparent.) I say Ah now we are at the crux of the matter. If you define scientific as algorithmic then only algorithmic models qualify. It also means that things like archeology are not science Peacefifthmonarchyman
January 24, 2015
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DDD, It is well known in modelling and analysis that transforming from one form to another is a reasonable approach. Here, log-probabilities are info measures and info as I outlined above can be directly counted off (esp. in bits, effectively what Orgel described) and can be refined using stochastic measures. For D/RNA, even were the info per codon only 1 bit (effectively, hydro phil/phob for instance), the set of proteins for simplest life takes us well past the 500 - 1,000 bit threshold. If you wand protein metrics that use the exploration of AA sequence space for proteins across the world of life as an index of variability on locus, try Durston et al, which I clipped from and noted on here, which builds on Shannon's H and I values already explained above. There are links to the 2007 paper, which gives Fits values for 15 protein families based on a very reasonable empirical process. The fits metric they give measures info in light of what is flexible to what extent. But of course this is a case where no information, evidence or logic will move those locked into Lewontin's a priori evolutionary materialism. Only public collapse of the system will, as happened for Marxism. KFkairosfocus
January 24, 2015
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fifthmonarchyman, A few days ago, you wrote:
If I understand Kolmogorov complexity it is not about the effort it takes to describe something it is about the effort it takes to compute it
That's not correct, and you're making the same mistake when you write things like this:
The k-complexity using this approach is huge and grows forever as more detail is needed.
Kolmogorov complexity is about the length of the description, not about the length of the computation.keith s
January 24, 2015
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fifthmonarchyman: Pi*r^2 is less complex than r^2*(4*(1 – 1/3 + 1/5 – 1/7 + …) Don’t you agree? Yes, given that pi is part of the description language; but your claim was that the k-complexity of the expansion is huge, and essentially unbounded. That claim isn't true. It's simple and finite. fifthmonarchyman: It’s not a God of the gaps argument it’s a argument for the less complex model. By that standard the simplest model of planetary movement is God did it, much simpler than gravity (as long as you don't have to include the complexity of God did it). Indeed, by that standard, the simplest description of every single phenomenon in the entire universe, from the smallest quantum interaction to why Mabel turned into the Five-and-Dime, to the large-scale structure of the universe is God did it (as long as you don't have to include the complexity of God did it). (Of course, that's not a scientific explanation, or even a scientific description, but that should be apparent.)Zachriel
January 24, 2015
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Zac says, The model includes the oracle, obviously. I say, Just as Pi*r^2 includes Pi. K complexity speaking Pi*r^2 is less complex than r^2*(4*(1 – 1/3 + 1/5 – 1/7 + …) Don't you agree? You say, That’s a novel use of God of the Gaps, though! I say, It's not a God of the gaps argument it's a argument for the less complex model. You say, You can’t use the term K-complexity and invent a new meaning. I say, No new meaning here. I talking about the the length of the shortest possible description of the model to explain the panorama of life. You say The decimal expansion of one divided by three is algorithmically simple. I say, So? what does a non halting decimal expansion of 1/3 have to do with a process that can't be modeled via an algorithm? peacefifthmonarchyman
January 24, 2015
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fifthmonarchyman: I never said there was necessarily no complexity in Turing Oracles it’s just there is no additional K-complexety in a model that contains them. The model includes the oracle, obviously. That's a novel use of God of the Gaps, though! fifthmonarchyman: It is simple to state that a series begins but very very difficult to say when it should end K-complexity is a proper name. You can't use the term K-complexity and invent a new meaning. The decimal expansion of one divided by three is algorithmically simple.Zachriel
January 24, 2015
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Zac says, Just because you call it a black box doesn’t mean it doesn’t entail complexity. I say, I never said there was necessarily no complexity in Turing Oracles it's just there is no additional K-complexety in a model that contains them. There is a difference You say, Your expansion is a simple series, which is algorithmically simple. I say It is simple to state algorithmically that a series begins but very very difficult to say when it should end, peacefifthmonarchyman
January 24, 2015
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